Development of the Prediction Graph Method Under Incomplete and Inaccurate Expert Estimates
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DEVELOPMENT OF THE PREDICTION GRAPH METHOD UNDER INCOMPLETE AND INACCURATE EXPERT ESTIMATES
Yu. Ya. Samokhvalov
UDC 519.17
Abstract. The author considers the mechanisms to process fuzzy experts’ estimates in forecasting the time and possible solutions of scientific problems. The distribution function of the runtime probability is proposed. This function allows constructing the continuous, integral distribution of a random variable on its total domain, based on the aggregate of discrete interval beta distributions. As the consistency measure of the fuzzy estimates, the coefficient of variation of the left- and right-hand boundaries of the time interval is used. Application of the Monte Carlo method to find the expected expenses for the problem solution is described. Keywords: prediction, prediction graph, goal attainment time, beta distribution, expertise, experts’ estimates, fuzzy estimates, Monte Carlo method. INTRODUCTION Academician V. M. Glushkov proposed the prediction graph method (PGM) in 1969 to predict scientific developments used in creating information processing facilities and assessment of perspectives of the development of computer engineering [1]. It can be efficiently applied to solve problems with a high degree of uncertainty, for example, determining the ways and results of scientific and technical progress, forecasting and planning of complicated social and economic processes, as well as scientific and engineering operations necessary to implement innovative projects in various fields. Using PGM allows generating sets of alternatives of scientific and technical development and finding optimal ways of goal attainment. An important part of the method is collective expertise on generating a set of original problems and determining the time of their solution. Point time estimates are used in this case. However, in practice, it is much easier psychologically for a person to make a fuzzy interval estimate of the time of onset of some event than to specify a value. Another important feature of PGM is the assumption about linear distribution of the runtime of operations, which is not always justified, especially for large time intervals. In order to extend the capabilities of the PGM, the paper [2] considers mechanisms of processing fuzzy estimates in generating discrete distributions of goal attainment time. In the present paper (which develops those studies), we will propose a technique to take into account incomplete and fuzzy expert estimates in constructing continuous empirical distributions, which allows making a more exact prediction of probable time and ways of solution of these problems. PROBLEM STRUCTURIZATION To explain the essence of the proposed approach, we will consider it in the context of PGM in the solution of the following problem [1]. Taras Shevchenko National University of Kyiv, Kyiv, Ukraine, [email protected]. Translated from Kibernetika i Sistemnyi Analiz, No. 1, January–February, 2018, pp. 84–92. Original article submitted March 5, 2017. 1060-0396/18/5401-0075 ©2018 Springer Scie
